52edt - Revision history

ArrowHead294 at 13:05, 10 April 2025

2025-04-10T13:05:53Z

← Older revision		Revision as of 13:05, 10 April 2025
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	{{ED intro}}		{{ED intro}}

	It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not exceptionally accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[~~13edt\|~~13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[~~The_Riemann_Zeta_Function_and_Tuning~~#Removing primes\|no-twos zeta peak edt]].		It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not exceptionally accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[the Riemann zeta function and tuning#Removing primes\|no-twos zeta peak edt]].

	== Harmonics ==		== Harmonics ==

ArrowHead294 at 19:11, 20 February 2025

2025-02-20T19:11:47Z

← Older revision		Revision as of 19:11, 20 February 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not ~~super-~~accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[13edt\|13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak edt]].		It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not exceptionally accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[13edt\|13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak edt]].

	== Harmonics ==		== Harmonics ==
Line 500:		Line 500:
	\| 365.761		\| 365.761
	\| 369.231		\| 369.231
	\| ~~−3~~.47		\| −3.47
	\|-		\|-
	\| 512.065		\| 512.065
Line 512:		Line 512:
	\| 1243.586		\| 1243.586
	\| 1246.154		\| 1246.154
	\| ~~−2~~.168		\| −2.168
	\|-		\|-
	\| 1389.89		\| 1389.89
Line 524:		Line 524:
	\| 2121.411		\| 2121.411
	\| 2123.077		\| 2123.077
	\| ~~−1~~.666		\| −1.666
	\|-		\|-
	\| 2633.476		\| 2633.476

ArrowHead294: Formatting

2024-11-13T13:53:03Z

Formatting

Show changes

Lériendil: removed falsehood

2024-10-09T11:29:14Z

removed falsehood

← Older revision		Revision as of 11:29, 9 October 2024
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	{{Infobox ET}}		{{Infobox ET}}
	The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 11-limit, so that it tempers out the same commas as ~~[[26edt\|26edt]] in the 11-limit and~~ [[13edt\|13edt]] ~~in the 7-limit~~. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak edt]].		The 52 equal division of 3, the tritave, divides it into 52 equal parts of 36.576 cents each, corresponding to 32.808 edo. It is something of a curiosity as it really needs to be considered as a 29-limit no-twos system. While not super-accurate, it gets the entire no-twos 29-limit to within 18 cents. It is distinctly flat, in the sense that 5, 7, 11, 13, 17, 19, 23 and 29 are all flat, so using something other than pure-threes tuning might be advisable. It is contorted in the 7-limit, so that it tempers out the same commas as [[13edt\|13edt]]. Other commas it tempers out includes 121/119, 209/207, 247/245, 275/273, 299/297, 325/323, 345/343, 363/361, 377/375, 437/435, 495/493, 627/625, 665/663, 667/665, 847/845, 1127/1125, 1311/1309 and 1617/1615. It is the eleventh [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak edt]].

	== Harmonics ==		== Harmonics ==

Lériendil: /* Harmonics */

2024-10-08T15:25:18Z

Harmonics

← Older revision		Revision as of 15:25, 8 October 2024
Line 3:		Line 3:

	== Harmonics ==		== Harmonics ==
	While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it ~~is notable for mapping~~ 11, 13, 19, and 29 ''slightly'' better than 26edt, giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].		While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it still maps 11, 13, 19, and 29 ''slightly'' better than 26edt, which is notable for giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].
	{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}

Lériendil: /* Harmonics */

2024-10-08T15:25:01Z

Harmonics

← Older revision		Revision as of 15:25, 8 October 2024
Line 3:		Line 3:

	== Harmonics ==		== Harmonics ==
	While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11, 13, and 19 ''slightly'' better than 26edt, giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].		While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11, 13, 19, and 29 ''slightly'' better than 26edt, giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].
	{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}

Lériendil: /* Harmonics */

2024-10-08T15:24:39Z

Harmonics

← Older revision		Revision as of 15:24, 8 October 2024
Line 3:		Line 3:

	== Harmonics ==		== Harmonics ==
	While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].		While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11, 13, and 19 ''slightly'' better than 26edt, giving them (despite being nearly half a step off in the case of 11) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].
	{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}

Lériendil at 21:16, 7 October 2024

2024-10-07T21:16:00Z

← Older revision		Revision as of 21:16, 7 October 2024
Line 3:		Line 3:

	== Harmonics ==		== Harmonics ==
			While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].
	{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}

	While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].

	== Intervals ==		== Intervals ==

Lériendil at 20:21, 7 October 2024

2024-10-07T20:21:41Z

← Older revision		Revision as of 20:21, 7 October 2024
Line 6:		Line 6:
	{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}

	While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]].		While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]], which is a record unbeaten until [[144edt]].

	== Intervals ==		== Intervals ==

Lériendil at 20:20, 7 October 2024

2024-10-07T20:20:04Z

← Older revision		Revision as of 20:20, 7 October 2024
Line 3:		Line 3:

	== Harmonics ==		== Harmonics ==
	{{Harmonics in equal		{{Harmonics in equal\|52\|3\|1\|intervals = prime\|columns = 9}}
	\| ~~steps =~~ 52		{{Harmonics in equal\|52\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	\| intervals = ~~integer~~
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 52
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	\| start = 12
	\| collapsed = 1
	\| intervals = ~~integer~~
	}}

	==Intervals==		While 52edt does not improve much on [[26edt]]'s mapping of the odd primes, it is notable for mapping 11 ''slightly'' better than 26edt, giving it (despite being nearly half a step off) a flat tendency in keeping with all the other odd primes, which allows 52edt to be the first edt that is [[consistent]] to the no-twos 29-[[throdd limit]].

			== Intervals ==

	{\| class="wikitable"		{\| class="wikitable"